In a wireless communication system, CPE is usually caused by phase noise and uncompensated frequency offset. CPE causes constellation rotation, which may severely degrade the performance of an orthogonal frequency division multiplexing (OFDM) system, especially an OFDM system with high modulation order and high carrier frequency. Pilot signal based CPE estimation is often used to compensate for such constellation rotation. Due to lack of a sufficient number of pilot signals, decision directed common phase error estimation (DD-CPE) has been proposed to further improve the CPE estimation quality. A typical approach to DD-CPE uses the hard decision of the detected transmit signal as known pilot signals to improve CPE estimation quality.